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The number of order-preserving maps between fences and crowns

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Abstract

We compute the number of order-preserving and -reversing maps between posets in the class of fences (zig-zags) and crowns (cycles).

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References

  1. Currie, J. D. and Visentin, T. I. (1991) The number of order-preserving maps of fences and crowns,Order 8, 133–142.

    Google Scholar 

  2. Duffus, D., Rödl, V., Sands, B., and Woodrow, R. (1992) Enumeration of order preserving maps,Order 9, 15–29.

    Google Scholar 

  3. Farley, J. D. (1992)Order-Preserving Maps between Posets in the Class of Crowns, Fences, and Chains, unpublished.

  4. Goldberg, S. (1958)Introduction to Difference Equations with Illustrative Examples from Economics, Psychology, and Sociology, Wiley, New York.

    Google Scholar 

  5. Parol, K. and Rutkowski, A. (1993) Counting the number of isotone selfmappings of crowns,Order 10, 221–226.

    Google Scholar 

  6. Rival, I. and Rutkowski, A. (1991) Does almost every isotone self-map have a fixed point? inExtremal Problems for Finite Sets, Bolyai Soc. Math. Studies,3, Visegrád, Hungary, pp. 413–422.

    Google Scholar 

  7. Rutkowski, A. (1991)On Strictly Increasing Selfmappings of a Fence. How Many of Them Are There? preprint.

  8. Rutkowski, A. (1992) The number of strictly increasing mappings of fences,Order 9, 31–42.

    Google Scholar 

  9. Rutkowski, A. (1992) The formula for the number of order-preserving selfmappings of a fence,Order 9, 127–137.

    Google Scholar 

  10. Stanton, R. G. and Cowan, D. D. (1970) Note on a ‘square’ functional equation,SIAM Review 12, 277–279.

    Google Scholar 

  11. Zaguia, N. (1993) Isotone maps: enumeration and structure, inFinite and Infinite Combinatorics in Sets and Logic, N. W. Sauer, R. E. Woodrow, and B. Sands (eds), Kluwer Academic Publishers, Dordrecht, pp. 421–430.

    Google Scholar 

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Communicated by A. Rutkowski

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Farley, J.D. The number of order-preserving maps between fences and crowns. Order 12, 5–44 (1995). https://doi.org/10.1007/BF01108588

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  • DOI: https://doi.org/10.1007/BF01108588

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